Professor O'Leary gave his annual lecture on principles of
bridge-building.

He began by describing the forces on a typical bridge structure,
with center
loading and side supports:

The effect of the load, and the balance of "bending moments" [whatCivil Engineers call "torques"] results in compression on the topmembers, and forces of expansion at the bottom.

The maximum stress [force per unit area] smax
on a board of width b, and height h, and length L is proportional to
the length
L, inversely proportional to the width b, and inversely proportional to
the
square of the height h:

smax µ L /
b h2

Furthermore, the bending displacement d at the
center is proportional to the following:

dµ
L3 / (b
h3)

As a consequence, we can make smax and dsmall
by making the height h large.

The buckling formula obtained by Euler
is

Pcritical = p2 E /4 I/L2

where the parameter I for a rectangle
is

I = b h3/12

A beam buckles under compression about
the "weak axis", rather than
the "strong" axis.

Another important design principle is
that "triangulation" makes
very stable structures, whereas non-triangular regions can more easily
become
deformed under stress.

Comments by Alex Junievicz: J. O'Leary showed that the
bending
of a meter stick depended upon direction. Physics teachers call
the
bending torque, but civil engineers use the term Moments. The term
torque has a
different application to civil engineers. The problem in a bridge
failure
is usually twisting and x cross members are used in the base, top and
entrance
to the bridge. The top and bottom of an I beam are
sometimes
laminated to add thickness providing more strength.

He showed that a foam stick when presses bend and broke when pressure
applied
laterally

Note--Like a strip of paper it is strong in one plane and care must be madeto prevent buckling (twisting) failures Note: bridges often fail by twisting,rather than from material failure.

New Rules-abutments are possible. Now the bottom (or resting surface) can befixed, as in the above one had to be variable, not it could be fixed andallow less materials used to prevent stretching when using an arch.

---------Compression vs Tension ------------

at the top there will be a force to compress; at the bottom there will beforce to spread

Note: I saw an question someone had on a test where a locomotive 4
times the
weight of a flat car hit and coupled, at 10Km/hr. My first thought was
that
there was a derailment and no conservation of movement on the tracks as
they
were dragged. I asked O'Leary's associate who seemed to be
knowledgeable about
Railroads....Coupling speed is done below 5 and at 10 damage may be
result. I
was interested in the comment that the power is much greater in toy
trains that
there may not be a realistic modeling.

07 December 1999: Eduardo De Santiago, Assistant Professor in
IIT's
Department of Civil and Architectural Engineering
introduced himself and explained that structural engineers design not
only
bridges, but are involved in design of nearly all structures:
buildings, space
platforms, dams, ships, antennas,... He soon had us involved in
answering
questions.

What is a bridge?

How would you define it?

What is its function?

Dialogue established that a bridge provided a way for things (traffic,
people,
etc) to move across a chasm, river, etc. Consider a simple bridge: a
plank
supported at each end. If a load (person) stands at its center, what
happens? A
student provided an answer: It bends. And so it went. With a
few
sketches, Prof De Santiago soon had us considering bending moments (M)
and shear
forces (V) - both internal forces - and how they affect the plank. We
defined
internal stress from a sketch of the distribution of forces across a
section of
the plank, with the NA (neutral axis) on the geometric axis.

In less than an hour of give-and-take, he led us to develop an
intuition for
the factors that affect the strength of structures, and to the truss
bridge.
We came to understand these terms: floor beam, panel, bottom and
top chords,
portal bracing, internal bracing.

Three tips offered by Prof. De Santiago:

maintain symmetry

minimize the number of connections or joints

craftsmanship is very important

21 November 2000 Eduardo De Santiago [IIT Civil and architectural
Engineering]
presented the Bridge Design Lecture, in preparation of the Bridge
Contest [http://www.iit.edu/~hsbridge/]
to be held at IIT on 13 February 2001. He said
that the
simplest type of bridge is the "plank bridge" bridging a gap while
supported on both ends. When you stop in the middle of the plank,
it sags
under your weight. The most noticeable effect is that of the bending
moment, which causes the plank to "curl up". These bending
moments are the most evident in bridge design, although shear forces
[transverse
action-reaction pairs at opposite ends of the board] are also
important. The
bending moment causes the top of the plank to be compressed and the
bottom to be
extended. The bending moment produces the greatest stresses at the top
and
bottom of the plank and decrease to zero at center. Therefore,
the
material in the center of the plank is being "wasted", since the
greatest stress [force per unit area] is at the top [compression] and
bottom
[extension].

We may make a bridge more efficient by building a hollow beam with a
few
vertical supporting members [like a ladder turned on its side].
This
construction reduces the effect of the bending moment, but increases
that of
shear stress. One may reduce the effect of shear forces by
putting
diagonal brace members into the network.

The object of design of wooden bridges is to convert bending moments
and shear
forces into longitudinal or axial forces [extension or compression],
because
wood is very strong under these forces. Also, we reduce the effect of
shear by
using triangles rather than rectangles, because rectangles collapse
easily under
shear, whereas triangles do not. Thus, the bridge geometry should
consist
entirely, or almost entirely, or triangles. In the above figure, you
can remove
the end members, which are subject to practically no stress, to
simplify the
construction to the following, known as a truss

A bridge consists of trusses on the sides, as well as a deck on the
bottom.
To avoid a collapse at the top, you should include bracing at the top,
again
consisting of triangles like the first figure. You should line up
vertical
joints exactly with horizontal joints to avoid "punch through". There
should also be lateral bracing at the top, to avoid shear in
the
transverse structure.

The bridge should be "left-right symmetric", since is one side is
weaker than the other it will break first. Remember that the
weakest part of
the bridge always breaks first under loading. These bridges are
operating is
a "near failure zone", which is not the regime in which large bridges
are designed to operate. Engineers are necessarily conservative in
their
designs, and one should become an "anti-engineer" to win the contest.

These bridges may undergo "buckling", since wood is more resistant
to tension than to compression. Under compression, a "slender" piece
may buckle. Therefore, one should keep the compressional members short
and fat.

Real bridges are also subject to "impact loads", produced by fast
moving trains, trucks, winds, and even earthquakes. They can be ignored
in the
contest, so long as you remember "not to drop the weights on the
platform", etc.

In the San Francisco Earthquake more than a decade ago, the lower
deck of the
Bay Bridge collapsed under action of a wave set up by the earthquake.
The
structural members of the bridge remained sound, however.

30 January 2001 Earl Zwicker (IIT)
indicated that National Engineers Week will occur during the
period 18 -
24 February 2001.
The IIT Bridge Contest http://www.iit.edu/~hsbridge/
is officially connected with this celebration, and contest winners will
be
invited to a special banquet during that week. National Engineers
Week,
sponsored jointly by IBM and NPSE, has an official
website, http://www.eweek.org/.
The national organization is sponsoring the Future City Competition,
as
described in the website http://www.futurecity.org/.

20 November 2001: Eduardo de Santiago (Civil and Architectural
Engineering, IIT)
Bridge Design
Lecture for 2002 IIT Bridge Contest [http://www.iit.edu/~hsbridge/database/search.cgi/:/public/index]Eduardo said that the goal of a Structural Engineer
is to predict the
forces acting on structures, and to determine whether those structures
will
collapse. He limited the discussion to Truss Bridges,
addressing these
basic questions:

Why do they look the way they do?

How do we make them stronger?

An old-fashioned bridge design might amount to putting a plank [or a
tree] across a gap
between two supports, as shown here:

This is not a very good bridge design, as can be seen in the "worst
case" scenario by putting a
significant load at the middle of the bridge. The bridge will bow
in the
middle if the load is substantial enough, because of the Shearing
Force
and the Bending Moment.

The shearing force on a small segment acts "up" at one
end and "down" at the other end, and tends to "slice through" the
segment.

The bending moment on a small segment acts clockwise on
one end and counterclockwise on the other end, and tends to "bend" the
segment.

The Bending Moment is most evident in practice; the plank bends as
you walk
across it. As viewed by a termite inside the middle of the plank the
force
changes gradually from compression to extension as you go through the
plank from
top to bottom, as shown:

From an engineering viewpoint, the material along the edges of the
plank is under the
greatest distress [stress], so that it would constitute an improvement
to "hollow out the
beam":

However, in such a case, the top part of the beam would carry
all the
load, and the bottom part would
support nothing. Therefore, we insert vertical supports
to transfer the
load from the top to the bottom:

The shear forces would then cause a problem, and we must add
diagonal members to transfer
both
horizontal and vertical forces. It is the vertical
components that serve to reduce
shear forces:

Craftsmanship is important in preparing these joints, in that it
is important that the pieces fit
together tightly, and that the joint members line up so that their
centers meet at a point.
The fundamental principle of Truss Design is to replace all shear
and bending
forces with compression and extension forces, and to
reduce the
structure to a series of triangles. There are several
different
types of basic bridge designs, such as these:

A great deal of information is provided at the West Point
Bicentennial Engineering Design Contest website, http://bridgecontest.usma.edu.
In particular, you can design your bridge, and test it to find how and
when it
will fail. Also, you can download the following packet from that
website:

Designing and Building File-Folder Bridges: A
Problem-Based Introduction to Engineering by Stephen J Rossler

This book provides students with an opportunity to learn how engineers
use math, science, and technology to design real structures. It is
intended primarily for high school students, but
those in lower grades should be able to complete all but Learning
Activity #3, which requires
the application of geometry, algebra, and some basic trigonometry.

Eduardo mentioned that cross-bracing between trusses is required
at their tops and bottoms.
Eduardo gave the following tips and pointers:

Make as few joints as possible.

Be sure that there is a good fit at all joints.

For crossed pieces, it is better to notch them slightly and glue
them for a
better fit, but don't make another joint there.

Be sure to glue doubled sticks all along their lengths, and not
just at the
ends.

He closed with the following observations:

Buttresses are good for bridges that permit support below the
roadway, as is not often allowed in contests.

Every bridge begins in the mind of an engineer.

In earthquake engineering, the idea is to save the people,
even if the structure is severely damaged. The idea is to
make the building "ductile" (energy absorbing), and not necessarily
"stiff". This way, the building can absorb energy without collapse,
although it may be unusable after the earthquake. In a similar
spirit, modern cars have "crumple zones" that are meant to crush and
absorb energy, in contrast to old cars that remain intact in a
collision but pass energy along to the occupants

04 December 2001: Ann Brandon (Joliet West HS, Physics)
Ann passed out a newspaper article describing an
internet-based,
virtual bridge building contest sponsored by the U S Military
Academy at West
Point, NY, using West Point Bridge Designer computer
software
available without cost at the contest website,
http://bridgecontest.usma.edu.
Students may compete either individually or in teams in this contest,
which
marks the bicentennial of the USMA. The prizes to winners
are rather
generous:

$15K [First], $10K [Second], and $5K
[Third].

You may also obtain information by email: ic7097@usma.edu
or by telephone at 1 - 845 - 938-2548. Thanks, Ann!

19 November 2002: Professor Eduardo De Santiago [Civil and
Architectural Engineering, IIT] Bridge Design
Eduardo De Santiago
made his fourth annual presentation before SMILE and guest
students and
teachers on "How to be a structural engineer in
one lesson"! He began by posing the following difficult question:

When and where will a given contest bridge fail?

He remarked that the answer to this question depends upon the details
of the contest
rules, craftsmanship in constructing the bridge, and other factors,
although it seems that all good
bridges up to now have been truss bridges. We will not repeat the
discussion of why truss bridges
are good, but refer to the relevant SMILE write-ups of 1999
[ph120799.htm],
2000 [mp112100.htm]
and 2001 [mp112001.htm]. [See
also the Bridge Building Contest Home Page: http://www.iit.edu/~hsbridge/database/search.cgi/:/public/index]
Instead,
we will simply list the relevant points that he made, in bullet form.

To design a bridge for center loading, an optimal bridge will be
symmetric about the center;
that is, if your bridge is not symmetric, you are wasting material. In
general, you should have
a good understanding of the points at which the bridge may be loaded.

When a bridge is supporting an external load, internal forces are
developed in various parts
of the bridge. Civil engineers analyze these forces in terms of bending
moments and internal shear forces.
A shear force tends to sever a beam, whereas a bending moment induces a
deformation of
the beam into a "smile" or a "frown". In general, bending moments are
more significant than
shears for bridge design.

If you place a load on a horizontal plank placed between two
abutments, the plank bows downward.
In this situation the top part of the plank is under compression,
and the bottom part of the plank
is under tension. The "neutral axis" running horizontally along
the center of the plank is under
relatively weak internal forces. This idea is the basis for the "I
beam" [transverse cross-section
shaped like an I], in which the material is located primarily at
the top and bottom of the beam,
where the greatest internal stresses are found.

Suppose we make a bridge that looks like a ladder turned on its
side:

This bridge will be resist bending, but will be very vulnerable to
shear. We use trusses [diagonals] to handle shear forces efficiently.

Here is a typical truss bridge panel

The two good things about trusses are (1) that they can handle shear
forces efficiently, and (2) that truss bridges --- assuming ideal
"pin connections" --- are completely solvable, as well as generally
strong
structures. Note that the "triangulation" provides strength by
preventing "buckling" of the bridge. [Since the ends of the bridge are
supported by the abutment and do not experience a bending moment,
a triangular portion at each end, being unnecessary, is removed.]

A truss bridge is made by connecting two side panels, with
cross-bracing and connections to provide
triangulation at the top. In addition, portal bracing is required at
the top to eliminate side-sway.

As a material, wood is strong under tension, but has a strong
tendency toward
buckling under compression. Long, thin pieces of wood may be
laminated by
gluing them together along their entire length. This is
especially
important for the bottom members of the bridge.

You should minimize the total number of joints, and be sure that
the joints fit
together snugly without gaps, before gluing them. Remember that
you are
trying to obtain strength through triangulation. Alignment of
joints is critical for building strong contest bridges.

In practice, gusset plates may be used for strengthening
joints in steel
truss bridges, but these are probably not practical for contest
bridges.

It is better to have "butt joints" with the full member resting
on top
of the piece below, so that the wood, rather than merely the glue, is
helping to
support the weight of the bridge.

You have to be sure that your weight platforms will support the
weight by
themselves, since there is the possibility of a "punch out", in which
the bridge remains largely intact, while the platform punches through
to release
the weights.

Some experimentation in the Seattle area has suggested that the
best glue
for contest bridges is ordinary wood glue [Elmer's Glue™?] , rather
than the
more expensive varieties.

If weight must be supported below the roadbed, you can build an
inverted truss.
It is important to have bracing below ground level at the abutments.
Remember that
the Romans understood the arching effect, and also learned [sometimes
the hard way]
that you must have the arch well attached to prevent buckling. You can
build an
inverted arch, as well as the usual kind.

Structural engineers are required to over-design bridges by
safety factors, so that
a 1000 kg load bridge will actually support 1500 kg, etc. Such caution
is, or course,
a sure way to lose bridge contests. The perfect contest bridge would
resemble the legendary
One Horse Shay [For details see THE DEACON'S MASTERPIECE OR, THE
WONDERFUL "ONE-HOSS SHAY": A LOGICAL STORY by Oliver Wendell
Holmeshttp://www.ibiblio.org/eldritch/owh/shay.html]
That is, it would shatter to smithereens when it failed, since
all its members
would be equally pushed to the limit.

Truss bridges are limited as to the distances they can span. For
longer spans, either cable
stay bridges or suspension bridges are required.

Good luck to one and all on your bridge building!

A great deal of information is provided at the West Point Bridge
Design
Contest website, http://bridgecontest.usma.edu/index.htm.
In particular, you can design your bridge, and test it to find how and
when it
will fail. Also, you can download the following packet from that
website:
Designing and Building File-Folder Bridges: A Problem-Based
Introduction to Engineering by Stephen J Rossler
This book provides students with an opportunity to learn how engineers
use
math, science, and technology to design real structures. It is intended
primarily for high school students, but those in lower grades should be
able
to complete all but Learning Activity #3, which requires the
application of
geometry, algebra, and some basic trigonometry. A windows-based
software
package is also available at that website; see
http://bridgecontest.usma.edu/download.htm.

02 December 2003: Professor Eduardo De Santiago [IIT: Civil
and Architectural
Engineering] Building
Lighter,
Stronger Bridges
This was without doubt Eduardo's most beautiful presentation
yet!
In preparation for the 28th Annual Chicago Regional Bridge
Building Contests, teachers and their students joined our
SMILE
meeting for Eduardo's fifth annual presentation on building a
strong yet light bridge.
Eduardo's previous lectures were
given in 1999 [ph120799.htm],
2000 [mp112100.htm],
2001 [mp112001.htm],and
2002 [mp111902.html].---
they dealt with the same ideas

He began by making a sketch on the
board showing how a cave person would use a fallen tree as a primitive
bridge to walk across a stream; a bridge takes a load
from one point to another without breaking. Then he pointed out that a
truss is a simple and efficient construction,
relatively easy to analyze. He introduced the concepts of bending
moment, tension, and shear as three important forces
internal to a bridge, and he illustrated each concept with sketches and
by using whiteboard erasers
that he bent and
otherwise stressed. From then on, one set of ideas led to another.
Eduardo connected them with lucid sketches,
eraser-bending, and articulate discussion. Simple ideas led to
increasingly complicated combinations of ideas, and when we finally
arrived at a typical
truss bridge, we understood the physical ideas behind it.
He did not write down any
equations! He pointed out the need
for symmetry (to deal with forces from any direction) and the
need to minimize the number of
joints. And to have fun!

When
he had finished, he and some members of the Bridge Building
Committee spent time with students and teachers
one-on-one,
answering questions. What a wonderful, phenomenological
presentation, Eduardo! Thanks!

14 December 2004: Roy Coleman [Morgan Park HS,
physics]
Weighing Bridges for the Bridge ContestRoy's students have been asking him how to determine
whether their bridges weigh less than 28 grams, as required
under the rules for the 2005 Chicago regional bridge-building
contests [http://www.iit.edu/~hsbridge].
He showed a simple balance set up with a meter stick balanced with its
center on a cylindrical ball-point pen lying horizontally on the table.
A few nickel coins served as "precision weights". The mass
of each nickel is very close to 5 grams. Roy took
the bridge materials kit, placed it on one end of the meter stick
balance, placed 6 nickels on the other end of the stick, and
found a good balance. He therefore concluded that the mass of the
bridge materials was approximately 30 grams. Roy
showed that, by placing 5 nickels at an end of the meter stick
and one at 20 cm from that end, one can determine whether the
finished bridge weights less than 28 grams. Roy
mentioned that this was a good place to introduce a discussion of
torques and their role in static equilibrium.